OFFSET
1,2
FORMULA
a(n) = Sum_{k=0..n} (-1)^k*(4*n-k)!/(24^(n-k)*6^k)*binomial(n,k). [corrected by Georg Fischer, Sep 01 2022]
a(n) ~ sqrt(Pi) * 2^(5*n + 3/2) * n^(4*n + 1/2) / (3^n * exp(4*n+1)). - Vaclav Kotesovec, Oct 21 2023
MATHEMATICA
Table[(4*n)! Hypergeometric1F1[-n, -4*n, -4] / (2^(3*n) * 3^n), {n, 1, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*(4*n-k)!/(24^(n-k)*6^k)*binomial(n, k)) \\ Georg Fischer, Sep 01 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Shanzhen Gao, Feb 24 2010
STATUS
approved